All of the above is good advice so here is some information and rough "rules of thumb" that work for me. You can do your own maths regarding how much cider you are making etc ...
Store bought juice is typically low in acid (around 3 or 4 g/L or 0.3% -0.4%), after all, it is meant to be sweet. The suggested range for cider is 5 -7g/L, so as a guide, adding 1/2 to 1 teaspoon of malic acid per litre will make a heap of difference. It adds some "bite" to an otherwise insipid cider. Lime juice, lemon juice, etc, does the same thing and can be added at any time according to your taste.
Similarly with tannin. I have tried powdered tannin but didn't like it very much. Strong black tea at 1 teabag steeped in about 1/2 cup of boiling water per gallon is a good starting point (the boiling water wipes out any nasties in the tea). Both acid and tannin give the cider "mouthfeel".
There is some debate around adding nutrients. "Normal" juice typically has 80 -100 ppm of YAN (Yeast Assimilable Nitrogen) nutrient which yeast need. This is more than enough for yeast to carry out a complete fermentation. However, YAN in juice that has been in cold storage can deteriorate to as little as 20ppm of YAN so fermentation can stall once the yeast has run out of the YAN. This can also happen with late season apples from old unfertilised trees.
Around 10 ppm of YAN is needed for every 10 gravity points of fermentation (so SG 1.050 juice only needs about 50 ppm of YAN which it usually has). However, with "store bought" juice it can be worthwhile adding nutrients as an insurance against a stalled fermentation.
Nutrient products like DAP, Fermaid, etc. contain about 20% YAN. So depending on how much "insurance" you want, adding the appropriate amount can be worthwhile. 0.05g/L of DAP will provide 0.01g/L of YAN which is enough for 10 gravity points of fermentation. As a rough guide adding enough YAN to ensure fermentation of say, 50% of the sugar would need 0.5g (about 1/10 teaspoon) of DAP per gallon. So "1 tsp is often just what the yeast need" is about right for a typical 5 gallon batch. I sometimes add DAP as the juice from my apples (old unfertilised trees) sometimes stalls around 1.010. (This makes for a natural sweeter cider but if I want to bottle condition, extra YAN is needed).
Adding DAP at the start usually produces a very robust fermentation (confidence building for a first-time ferment!). There is a view that nutrient is best added halfway through fermentation (say, when racking to secondary if that is your process), so that the natural YAN is consumed first and the yeast don't get "overfed".
I hope this helps answer your questions.